Although contrast-enhanced magnetic resonance angiography (CE-MRA) is widely established as a clinical examination for the diagnosis of human vascular diseases, non-contrast-enhanced MRA (NCE-MRA) techniques have drawn increasing attention in recent years. NCE-MRA is based on the intrinsic physical properties of blood and does not require the injection of any exogenous contrast agents. Subtractive NCE-MRA is a class of techniques that acquires two image sets with different vascular signal intensity, which are later subtracted to generate angiograms. The long acquisition time is an important drawback of NCE-MRA techniques, which not only limits the clinical acceptance of these techniques but also renders them sensitive to artefacts from patient motion. Another problem for subtractive NCE-MRA is the unwanted residual background signal caused by different static background signal levels on the two raw image sets. This thesis aims at improving subtractive NCE-MRA techniques by addressing both these limitations, with a particular focus on three-dimensional (3D) femoral artery fresh blood imaging (FBI). The structure of the thesis is as follows: Chapter 1 describes the anatomy and physiology of the vascular system, including the characteristics of arteries and veins, and the MR properties and flow characteristics of blood. These characteristics are the foundation of NCE-MRA technique development. Chapter 2 introduces commonly used diagnostic angiographic methods, particularly CE-MRA and NCE-MRA. Current NCE-MRA techniques are reviewed and categorised into different types. Their principles, implementations and limitations are summarised. Chapter 3 describes imaging acceleration theories including compressed sensing (CS), parallel imaging (PI) and partial Fourier (PF). The Split Bregman algorithm is described as an efficient CS reconstruction method. The SPIRiT reconstruction for PI and homodyne detection for PF are also introduced and combined with Split Bregman to form the basis of the reconstruction strategy for undersampled MR datasets. Four image quality metrics are presented for evaluating the quality of reconstructed images. In Chapter 4, an intensity correction method is proposed to improve background suppression for subtractive NCE-MRA techniques. Residual signals of background tissues are removed by performing a weighted subtraction, in which the weighting factor is obtained by a robust regression method. Image sparsity can also be increased and thereby potentially benefit CS reconstruction in the following chapters. Chapter 5 investigates the optimal k-space sampling patterns for the 3D accelerated femoral artery FBI sequence. A variable density Poisson-disk with a fully sampled centre region and missing partial Fourier fractions is employed for k-space undersampling in the ky-kz plane. Several key parameters in sampling pattern design, such as partial Fourier sampling ratios, fully sampled centre region size and density decay factor, are evaluated and optimised. Chapter 6 introduces several reconstruction strategies for accelerated subtractive NCE-MRA. A new reconstruction method, k-space subtraction with phase and intensity correction (KSPIC), is developed. By performing subtraction in k-space, KSPIC can exploit the sparsity of subtracted angiogram data and potentially improve the reconstruction performance. A phase correction procedure is used to restore the polarity of negative signals caused by subtraction. The intensity correction method proposed in Chapter 4 is also incorporated in KSPIC as it improves background suppression and thereby sparsity. The highly accelerated technique can be used not only to reduce the acquisition time, but also to enable imaging with increased resolution with no time penalty. A time-efficient high-resolution FBI technique is proposed in Chapter 7. By employing KSPIC and modifying the flow-compensation/spoiled gradients, the image matrix size can be increased from 256×256 to up to 512×512 without prolonging the acquisition time. Chapter 8 summarises the overall achievements and limitations of this thesis, as well as outlines potential future research directions.